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cooling cost allocation in multifamily housing
Energy and Buildings 40 (2008) 689–696 www.elsevier.com/locate/enbuild
Key technologies on heating/cooling cost allocation in multifamily housing Ye Yao a,*, Shiqing Liu b, Zhiwei Lian a a
Institute of Refrigeration & Cryogenics, Shanghai Jiao Tong University, Dongchuan Road No. 800, Shanghai 200030, China b Institute of Mathematics and Physics, Zhejiang Normal University, Zhejiang 321004, China Received 4 February 2007; received in revised form 21 March 2007; accepted 13 April 2007
Abstract Heating/cooling cost allocation is of growing concern in many countries because it contributes much to the energy conservation of central airconditioning system. This paper intends to summarize the current studies and techniques on the heating/cooling cost allocation and discuss about the key problems to them. The contents mainly include the following parts: (1) probing into the methods of heating/cooling measurement; (2) establishing the calculation model for thermal billing; (3) presenting several typical systems for heating/cooling cost allocation. The significance of the paper is to help the engineers in this field have a good idea of the current development of heating/cooling cost allocation and promote the application of the relevant technologies to practice. # 2007 Elsevier B.V. All rights reserved. Keywords: Heating/cooling; Measurement; Thermal energy; Price; Cost allocation system
1. Introduction Heating/cooling cost allocation refers to certain accounting procedures designed to divide the energy costs in centrally heated/cooled multifamily buildings among the individual apartments on the basis of use. Heating/cooling cost allocation not only contributes to energy conservation [1], but also brings about many other social and economic benefits, such as decreasing vacancy rates, enhancing the rent levels and improving the comfort of tenants [2]. Heating/cooling cost allocation in apartment buildings was firstly developed in the Western Europe. In the early 1970s, the European Economic Communities has formulated implementation guidelines to encourage allocation of heating/cooling cost in multifamily housing. As of 1979–1980, approximately 70% of multifamily buildings of three or more units in Germany had such allocation systems [3]. Many other countries in Europe, e.g. France, Switzerland, Austria and Greece, also required measurement and allocation of costs for central heating/cooling systems in new constructions beginning in the early 1980s. In USA, Heating/cooling cost allocation in multifamily housing
* Corresponding author. Tel.: +86 21 34204263. E-mail address: [email protected] (Y. Yao). 0378-7788/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2007.04.023
began as a cottage industry in the early 1980s as a result of the 1979 oil embargo [4]. In China, with the development of economy and improvement of people’s standard of living, centrally air-conditioned buildings have been rising in recent years. In order to advocate the consciousness of energy conservation among people, the government of China has also urged the implement of thermal energy cost allocation in centrally air-conditioned buildings since the end of 1990s. This paper will summarize the existing technologies and discuss over the key problems on the heating/cooling cost allocation. The contents mainly include: (1) probing into the methods of heating/cooling measurement; (2) establishing the calculation model for thermal billing; (3) presenting several typical systems for heating/cooling cost allocation. 2. Methods of heating/cooling measurement Impartial cost allocation depends on effective measurement. Over the years, an increasing number of approaches have been developed to measure the thermal energy use of apartment supplied by a central heating/cooling system. They can be categorized into two types: the straightforward and the backstair. The straightforward method computes the thermal energy consumption of an apartment based on the running conditions of the terminal heating/cooling units in the apartment. The
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Nomenclature A B c C d G h i K M N P q Q R t T U V W Y z
area of heat transfer (m2) price of primary energy (US$/kJ) specific heat (kJ/kg) cost for yielding thermal energy (US$) humidity of air (g/(kg dry air)) flow rate of fluid (kg/s) enthalpy (kJ/kg) yearly interest rate of bank overall coefficient of heat transfer (kW/(m2 8C)) overhead expenses per hour (US$) number of apartments involved in thermal cost allocation price (US$/kJ) thermal output of individual units (kJ) total amount of thermal energy produced per hour (kJ) thermal loss (kJ) temperature (8C) total operating time of the central system in a year (h) fixed/floating/cost per hour (US$) initial investment (US$) amount of heat gain or loss of the jth apartment during the billing time bill for thermal cost of individual apartment (US$) life cycle of facilities (year)
Greek letters b correction factor of thermal metering due to location of apartment in the building Dt interval time of calculation (Dt = t/n (n is one big integer)) e coefficient of performance of boilers or heat pumps h proportion of thermal load due to exposed structures in the total of the building k correction factor of heat exchange of individual units Subscripts a air h/c heating/cooling i inlet/entering j the jth apartment jk walls between the jth apartment and its adjacent ones k the kth apartment o outlet/leaving w water we exposed wall of apartment wr interior wall or roof of apartments
measured parameters may include the following variables: the inlet/outlet water temperature, the waterflow rate, the airflow rate, the inlet/outlet air temperature and humidityas well as the running time of the individual heating/cooling units. However, the backstair method measures the parameters other than the above variables. It realizes the thermal metering through special algorithm. Since the straightforward method is easy to understand and be accepted by average tenants, the thermal meters available in market nowadays are mostly based on the straightforward method. 2.1. Examples of straightforward method 2.1.1. Actual-Btu meters Actual-Btu meters usually measure the inlet water temperature, tw,i, the outlet water temperature, tw,o, and the water flow rate, Gw, as well as the running time, t, of the heating/ cooling units in an apartment. The consumption of heating/ cooling of a single apartment, qh/c, during the running time, t, can be calculated by: qh=c ðtÞ ¼ cw
n X
Gw ðkDtÞjtw;o ðkDtÞ tw;i ðkDtÞjDt
(1)
k¼1
In principle, Actual-Btu meters are of high accuracy, typically 98% [1]. However, in practice their accuracy is not as high as expected, especially when small temperature drops across an individual apartment loop. Guinn and Hummer [5] found that the errors of Actual-Btu meters could be as high as 30%. Still, Actual-Btu is considered as the most accurate method for thermal metering. The biggest shortcoming of such meters is of relatively high investment and difficult maintenance. 2.1.2. Relative-Btu meters Relative-Btu meters only measure the inlet water temperature, tw,i, and the outlet water temperature, tw,o, as well as the running time, t, of the individual heating/cooling units. It is assumed that the water flow rate passing through the heating/ cooling units be invariable. In such case, the thermal energy output of the terminal units in an apartment can be counted by: qh=c ðtÞ ¼ cw Gw
n X
jtw;o ðkDtÞ tw;i ðkDtÞjDt
(2)
k¼1
Relative-Btu meters may be valid only if there is no zone water valve in each heating/cooling units that adjusts the passing water flow rate. Otherwise, the metering accuracy will typically achieve above 90%. Otherwise, the error may exceed 50% [1,6]. A variation of Relative-Btu is only to measure the temperature of water that leaves each apartment. The entering water temperature of each apartment can be taken as the same, which equals to the supply water temperature of the central heating/cooling system. Obviously, Relative-Btu meters will be much cheaper than the Actual-Btu ones. 2.1.3. LMTD meters The method measures the inlet air temperature, ta,i, the outlet air temperature, ta,o, the inlet water temperature, tw,i, the outlet
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water temperature, tw,o, and the running time, t, of the individual heating/cooling units. Then, use Eq. (3) to realize the thermal metering [7]: qh=c ðtÞ ¼ kh=c K h=c Ah=c
n X jLMTDðkDtÞjDt
(3)
k¼1
In Eq. (3), LMTD, namely Logarithmic Mean Temperature Difference, is usually used to calculate the heat transfer of the heat exchanger, which can be expressed by Eq. (3a): LMTDðkDtÞ ¼
½tw;i ðkDtÞ ta;o ðkDtÞ ½tw;o ðkDtÞ ta;i ðkDtÞ ln½ðtw;i ðkDtÞ ta;o ðkDtÞÞ=ðtw;o ðkDtÞ ta;i ðkDtÞÞ
(3a)
The most important step for the LMTD method is the determination of the total coefficient, K, and the heat transfer area, A, of the heating/cooling units. Since the total coefficient of heat transfer, K, is influenced by the flow rates of air and water, the LMTD meters are only fit for such systems that the water flow rate passing through the individual heating/cooling units changes very little. The airflow rates of the heating/ cooling units are usually divided into several levels. Each level of airflow rate will correspond to one value of heart transfer coefficient. When the consumer tunes the airflow rate from one level to another, the value of K will change correspondingly. Since LMTD just calculates the sensible thermal energy output of the heat exchanger, it will be much more accurate in heating season than in cooling one. In practice, the entering water temperature can be substituted by the supply water temperature of the boilers or the heat pumps. So, only three temperature sensors are needed for every apartment. 2.1.4. Air-side monitors The method mainly measures the conditions of inlet and outlet air of individual heating/cooling units. The measured parameters include: the inlet air temperature (ta,i), the inlet air humidity (da,i), the outlet air temperature (ta,o), the outlet air humidity (da,o), the airflow rate (Ga) and the running time (t). The thermal metering can be done using Eq. (4): n X Ga ðkDtÞjha;i ðkDtÞ ha;o ðkDtÞjDt qh=c ðtÞ ¼
(4)
k¼1
where ha;i ðkDtÞ ¼ ca ta;i ðkDtÞ þ ½2501 þ 1:84ta;i ðkDtÞda;i ðkDtÞ (4a) ha;o ðkDtÞ ¼ ca ta;o ðkDtÞ þ ½2501 þ 1:84ta;o ðkDtÞda;o ðkDtÞ (4b) Although air-side method is complicated and of high cost, it still has some merits such as convenience to install and maintain. In practice, the airflow rate, Ga, can be obtained from the level of airflow rate of the heating/cooling units. Hence, only two temperature sensors together with two humidity sensors are needed for this method.
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Another version of air-side method was put forward and studied in literature [8]. It only measures the temperature and the humidity of inlet air of individual heating/cooling units and realizes the thermal metering together with the other information that obtains from the central hydronic cooling/ heating systems through network communication. The method may be fit for such system where there are no local valves in the individual heating/cooling units. Theoretically, the errors of the method can be about 25% in most cases [8]. 2.1.5. Elapsed time meters The method just counts the running time of the heating/ cooling units in the apartment. Essentially, it does not measure the amount of heat delivered, but provide an estimate. Big metering errors will be caused by the elapsed time method because there may exist great differences among the terminal heat exchangers in thermal characteristic, and the conditions of cooling/heating water that enters into the apartments will be different from one to another. In spite of this, elapsed time meters are still popular in China due to their low investment. 2.2. Examples of backstair method 2.2.1. Comfort level monitors The idea of comfort level monitors is that ‘‘All residents with the same size apartment with the same average monthly setpoint pay the same amount.’’ Setpoint is used rather than space temperature because space temperature may be influenced by some factors, such as solar gain, the air infiltration from windows or doors. A comfort-based system using thermostat setpoint as an indication of system demand effectively eliminates building variables. The thermostat setpoint in each apartment is transduced from a potentiometer attached to the thermostat lever arm and then is transmitted to a central processor over building telephone lines. Comfort-based systems have been used and readily accepted by the residents in France for many years [4]. It would be more valid if the comfort level meters were used together with the excellent control system for indoor air temperature [9]. 2.2.2. Thermal metering based on load calculation The method counts the amount of thermal energy consumption in an individual apartment through calculating the heating/cooling load of the apartment during the use time. The measured parameters include the solar radiation intensity and the temperatures of indoor air and outdoor air. The authors ever studied the thermal metering method based on the theory of frequency response [10]. Experiments has been done in a residential building to manifest that heating/cooling load calculation may be a promising way in the thermal metering of residential apartments or office rooms. 3. Price of thermal energy A basic presupposition here is that optimal prices from a societal point of view should equal to short-range marginal costs (SRMC) of district cooling/heating generation [11]. These
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prices reflect the scarcity of resources in society, and are the best means for optimal resource allocation. However, such prices do not guarantee full cost coverage for the producer [12]. The price for cooling and heating is defined as the cost for every unit yielding thermal energy, which can be expressed as: Ph=c ¼
C h=c Qh=c
(5)
The cost of thermal energy, Ch/c, produced by the central heating/cooling system consists of two parts: one is named as fixed cost (Ufixed) that mainly includes the depreciation of facilities and the interest of investment and all the overhead expenses; the other is named as floating cost (Ufloating) that mainly includes the operating charges. C ¼ U fixed þ U floating
V½iði þ 1Þz =½ði þ 1Þz 1 þM T h=c
(7)
The floating cost, Ufloating, is correlative with the price of primary energy (B), the coefficient of performance of boilers or heat pumps (eh/c) and the total amount of thermal energy produced per year (Qh/c), which can be expressed as: U floating ¼
BQh=c eh=c
(8)
Combining Eqs. (5)–(8), the price of thermal energy produced by the central heating/cooling system can be written as: Ph=c ¼
(1) The initial investment of the central heating/cooling system, V; (2) The price of electrical energy or fuel, B; (3) The coefficient of performance of boilers or heat pumps, eh/c; (4) The amount of thermal energy produced the central heating/ cooling system per hour, Qh/c; (5) The yearly interest rate of bank, i; (6) The overhead expenses for management per hour, M.
(6)
According to the theory of engineering economy [13], the fixed cost per day, Ufixed, can be expressed as: U fixed ¼
Normally, the total operating time of the central heating/ cooling system in a year, Th/c, is settled by company. Thus, the price of thermal energy (Ph/c) is mainly related to the following factors:
V½iði þ 1Þz =½ði þ 1Þz 1 þ T h=c M B þ T h=c Qh=c eh=c
(9)
The price of thermal energy (Ph/c) in a day may change from hour to hour because the coefficient of performance of boilers or heat pumps (eh/c) fluctuates all the time. To illustrate the price model of thermal energy, one central air-conditioning system is taken as an example. The airconditioning system provides heating/cooling energy for 250 units apartments that are installed with FP600-type fan-coil units. The main equipments and initial investment of the system are listed in Table 1. The prices in Table 1 were provided by the East China Architecture Design Institution according to Chinese market. The exchange rate of US$ to RMB was set as 8.0. The coefficients of performance of the heat pump under different capacity ratio are shown in Table 2. The heat pumps, the cooling water pumps, the chilled/hot water pumps and the cooling tower are in operation during the cooling season, While in the heating season, the heat pumps are converted into the water-source ones and the cooling tower stops running. When the cooling/heating load demand exceeds 800 kW/900 kW, two heat pumps together with two cooling water pumps and two chilled/hot water pumps will be started.
Table 1 Equipments and initial total investment of one central air-conditioning system Items
Technical property
Number (set)
Investment (US$)
Screw heat pump
Rated cooling capacity: 774 kW Rated heating capacity: 897 kW Input electrical power: 160 kW
2
130,000
Cooling tower
Maximum water volume: 86.7 kg/s Input electrical power: 11.2 kW
2
15,000
Cooling water pump
Rated water volume: 87.5 kg/s Input electrical power: 30 kW
2
3,340
Chilled/hot water pump
Rated water volume: 70.8 kg/s Input electrical power: 22 kW
2
3,060
FP600 fan-coil unit
Heat capacity: 5.593 kW Input electrical power: 102.5 W
250
20,000
Pipes, valves and other fittings Charges for electrical distribution Charges for excess capacity of electricity Installment
– – – –
– – – –
14,700 32,712 20,445 21,500
Total
–
–
260,757
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Table 2 Coefficients of heat pump under different capacity rates Capacity rate (%) Compressor power input (kW) Cooling capacity (kW) ec Heating capacity (kW) eh
20 28.8 89.9 3.12 112.9 3.92
30 35.2 120.4 3.42 152.8 4.34
40 43.2 160.3 3.71 197.9 4.58
Otherwise, only one heat pump together with one cooling water pump and one chilled/hot water pump are operating. The cooling time of the system usually begins from 1 June to 1 October, and the heating time from 1 December this year to 1 March next year. The running time of the central heating/ cooling system in a day is set as 18 h, and the total operation time in a year is about 3180 h (Th/c = 3180 h). Assuming that the interest rate (i) is 0.005, the life cycle (z) is considered as 20 years, the overhead expenses (M) equals to US$ 15 h1, and the price of primary energy (B) is defaulted as US$ 0.1 kW h1, the hourly price of yielding thermal energy can be calculated using Eq. (9) with respect to the amount of yielding thermal energy and the hourly Coefficient of Performance (COP) of the heat pumps. The hourly cooling and heating energy produced by the heat pumps and the hourly COP of the system in one running day are plotted in Figs. 1 and 3, respectively. And the corresponding hourly price of cooling and heating energy are shown in Figs. 2 and 4, respectively. Seen from Figs. 1–4, the bigger amount of thermal energy produced by the central
Fig. 1. Hourly cooling energy produced and hourly coefficient of performance of the system in one day of August.
Fig. 2. Hourly price of cooling energy in the day of August.
50 54.4 210.5 3.87 260.6 4.79
60 68 277.4 4.08 337.3 4.96
70 82.4 348.6 4.23 422.7 5.13
80 100.8 439.5 4.36 529.2 5.25
90 128 600.3 4.69 701.4 5.48
100 160 787.2 4.92 910.4 5.69
heating/cooling system, the lower price of thermal energy will be. It accords with the general phenomenon of economics. 4. Individual thermal billing 4.1. Basic calculation method Based on the individual thermal metering and the price of thermal energy, the basic model for individual thermal billing, Yj, can be expressed as: R Y j ¼ Ph=c qh=c; j þ (10) N In Eq. (10), R denotes the thermal energy loss due to the heat exchange between chilled/hot pipes and the environment, which can be counted indirectly by Eq. (11): R ¼ Qh=c
N X qh=c; j
(11)
j¼1
Fig. 3. Hourly heating energy produced and hourly coefficient of performance of the system in one day of November.
Fig. 4. Hourly price of heating energy in the day of November.
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The basic model for thermal billing, in this paper, sticks to the principle that the tenants should pay equal cost for equal thermal energy use. In practice, some other detailed problems should be considered.
In residential building, the exposed structures may consume most of the heating/cooling energy of the apartment. Taking the apartment with the least exposed surface area as the standard one, the correction factor, b, for the other apartments can be expressed as:
4.2. Problem to indirect heat delivery In the apartment buildings, a certain amount of heat is delivered by indirect path, e.g. heat transferred through the wall from the warmer apartment to the other adjacent ones, and the warm air rising from lower apartments to the higher ones. These heat flows cannot be measured directly. So, proper adjustments for indirect heat delivery among the apartments should be made to guarantee the perfect allocation of thermal energy cost. The critical measure is to determine the static heat flow rates between neighboring rooms. Pakanen and Karjalainen [14] has focused on the heat transfer issues and put forward a new approach to solve it. Their approach is based on the proposed control techniques and the ARMAX-model describing dynamic behavior of heating/cooling power. The model is created for each room/flat of a building. Parameter values are identified using real-time measurements collected from each room/flat and its environment through a few days’ tuning. The prerequisite for successful estimation is the overall control and the precise adjustment of the room temperatures at specified level. When the heat delivery through the walls and roofs of apartments is taken into accounted, the billing Eq. (10) can be written as: R Y j ¼ Ph=c qh=c; j þ þ W j (12) N In Eq. (12), Wj is the amount of heat gain or loss of the jth apartment during the billing period, tbill: 8 m X > > K wr; jk A jk ð¯ta;k ¯ta; j Þ Heating time t > bill < k¼1 (13) Wj ¼ m X > > > tbill K wr; jk A jk ð¯ta; j ¯ta;k Þ Cooling time : k¼1
where m denotes the number of apartments that neighboring the jth apartment. ¯ta; j and ¯ta;k denote the mean indoor air temperature of the jth apartment and it adjacent ones during the billing time, tbill.
bj ¼
Awe; j Awe;standard Awe;total
(14)
where Awe,j, Awe,standard and Awe,total denote the area of exposed structure of the jth apartment, the standard apartment and the all apartments involved in the thermal energy cost allocation, respectively. Thus, the perfect individual billing equation may be written as: R Y j ¼ Ph=c ð1 þ bÞhqh=c; j þ ð1 hÞqh=c; j þ þ W j (15) N In Eq. (15), h is the ratio of heating/cooling load of the exposed structures to the total heating/cooling load of the building. To determine the value of h, the detailed design thermal load of the building can be referenced. 5. Typical system for thermal cost allocation Up to now, many advanced techniques have been applied to the heating/cooling cost allocation systems. Generally speaking, there are two types of system for the thermal cost allocation: one is network-based system; another is prepaid IC card system. 5.1. Network-based system Taking advantage of the technique of network, we can complete the remote thermal metering and charging without entering into the tenants’ apartment. Another merit of networkbased systems is that they can be fit for all metering methods and be propitious to improve the metering accuracy. Besides, through network, much useful information is recorded and saved real-timely with which the reasonable hourly price of thermal energy can be determined [15,16]. However, networkbased systems may have some shortcomings, e.g. relatively high investment, difficulty in maintenance and extend. In spite of their limitations, the network-based systems are still favored by people. Fig. 5 shows the schematic structure of the network-
4.3. Adjustment for the location of apartments The location in a building may produce important influence on the energy consumption of the apartments for heating/ cooling. Because apartments with different location in a building will have different exposed surface area, different air infiltration and different solar gain. These differences may cause substantial variations in the allocation bills from one apartment to another. For the sake of fairness, it is necessary to make the adjustment with respect to different location in the building such as the orientation, the floor, etc.
Fig. 5. Schematic for the thermal metering system based on the local network communication.
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based system for thermal metering and charging. In such system, the thermal meters with communication convertor are necessary. Obviously, the communication convertor will take the most important role in the network-based system. In this paper, two communication techniques, which may be potientially applied to the thermal metering and charging, are to be introduced briefly. 5.1.1. RS-485 communication It is well known that RS-485 is a comprehensive bidirectional and differential transmission data bus [17]. As a physical layer protocol, it provides half-duplex communication and multipoint links. The information can be sent or received through two wires. It has the features such as without charge accumulation, high capability of anti-jamming and long transfer distance. Although RS485 does not belong to field bus, it has strong life force because of the performance above. MAX485, as a kind of low-power transceiver for RS-485 and RS-232 communication, could be selected for the communication interface of the thermal meters. MAX485 sends and receives the information data by using only one transmission channel in a half-duplex mode The half-duplex mode has both merit and demerit. The advantage is that a transmission channel can operate using just two lines. This advantage must be weighed against the limitation that only one master on the sending side can operate at any given time. Fortunately, the limitation produces no influence on the work of network-based thermal metering and charging systems that are compose of one master machine and many sub-machines. The sub-machines, known as thermal meters, are responsible for the measurement of thermal energy consumption in individual apartment. They mainly include measurement component, computation component, data storage component and communication component with RS485 interface [18]. The master machine is usually in charge of many sub-machines (thermal meters). It can require communicating with any thermal meter in charge at any time through sending command. When one thermal meter receives the command, it will response to the master machine’s require and send the information in its memory chip to the master machine through RS-485 communication. The main task of the master machine is to monitor the thermal energy consumption of all apartments in a period of time, to determine the hourly price of thermal energy and to count the bills every tenant should pay for the thermal energy use. 5.1.2. Power line carrier communication A power line carrier (PLC) is communication equipment that operates at radio-frequencies, generally below 600 kHz, to transmit information over electric power transmission lines. The new communication technique has been developed very rapidly in recent years and been in wide field applications, such as energy services [19] and automatic remote meter reading [20,21]. The obvious advantage of power line carrier is that it need not construct an extra wiring, and hence save much labor force and time.The new ATL90 series Embedded PLC modem series is based on the Direct Sequence Spread Spectrum Technology [22]. The new technology in power line carrier
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communication is well known for its high immunity to electrical noise persistent in the power line. With the new solution, the form factor of the PLC modem is further reduced and its cost lowered. The Embedded PLC Modem is in the form of a ready-to-go circuit module, which is capable of transferring data over the power cable at the low voltage end of the power transformer of a 3-phase/4-wire distribution network. A pair of Embedded PLC Modems connected on the power line can provide low speed bi-directional data communication at a baud rate of 300/600 bps. It is built in a small form factor that can be easily integrated into and become part of the user’s power line data communication system. The modules provide bi-directional half-duplex data communication over the mains of any voltage up to 250 V ac, and for frequency of 50 or 60 Hz. Data communication of the modules is transparent to user’s data terminals and protocol independent; as a result, multiple units can be connected to the mains without affecting the operation of the others. The use of DSSS modulation technique ensures high noise immunity and reliable data communication. There is no hassle of building interface circuits. Interface to user’s data devices is a simple data-in and data-out serial link. It has a built-in on board ac coupling circuit, which allows direct and simple connection to the mains [20]. 5.2. Prepaid IC card system The outcome of the Prepaid integrated circuit (IC) card thermal metering system has changed the former paying way of the thermal energy thoroughly, from manually to automatically. The way it has changed brings much benefit to the heating/ cooling department. It not only strengthens the supervision, increases management efficiency, effectively prevents overdue bills, but also avoids the inconvenience of house call meter reading and decreases the capital of running the department. To make the prepaid IC card come to life, the most important point is to change the thermal meters that are now widely used, and make it easy for dismantling and card inserting. Besides, the thermal meter ought to have the function of automatic fee charging. In the Prepaid IC card thermal metering system: one user is assembled with one thermal meter and one card, to use thermal energy only by card. After the data in the card is transmitted to the thermal meter, the meter opens the valve and begins thermal supply, after the money is used up, it will automatically cut off thermal supply and you must buy thermal energy again to resume energy use. The working process of the IC card is depicted as follows: the users pay the fees to the thermal management department, which writes the amount of thermal into the IC card, and the users input the information of the IC card into the thermal meter, which can automatically begin thermal supply. During the period of thermal use, the microcomputer within the thermal meter will automatically check and subtract the used thermal energy, when the purchased thermal energy is used up, the intelligent thermal meter will cut off thermal automatically, and the user needs to buy thermal energy again. IC card can also record the operation
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conditions of the meter, to control total used thermal energy, total purchased thermal energy and the state of opening and closing of the valve by controlling computer or controlling software. 6. Conclusions This paper mainly aroused interest in the critical problems concerned about the heating/cooling cost allocation. The contents include: (1) Seven kinds of methods of thermal metering have been introduced in detail. At the same time, they are discussed and analyzed in terms of accuracy and investment. (2) The model of hourly price of thermal energy has been set up. One example is presented to expound the usage of the model. The results prove that the price model accords with the general phenomenon of thermal economics. The model will help us establish the reasonable and impartial price of thermal energy produced by the central systems of different kind. (3) The effective way of thermal billing of individual apartment is studied. Some field problems, such as the indirect heat delivery from one apartment to another and the adjustment for different location of apartment in a building, are discussed. The corresponding measures are suggested afterwards. (4) The typical systems for thermal cost allocation are presented. The network-based system, represented by the communication techniques of RS485 and power line carrier, and the prepaid IC card system are depicted in detail. Their technical properties are also introduced briefly.
References [1] W.L. Scott, Energy conservation from individual heat use monitoring in multifamily properties, ASHRAE Transactions 97 (1) (1991) 396– 404. [2] D. Palermini, D. Hewitt, Economic and social impacts of converting to tenant metering in multifamily housing, ASHRAE Transactions 97 (1) (1991) 391–395. [3] M.J. Hewett, H.L. Emslander, M.J. Koehler, Heating cost allocation in multi-family buildings: energy savings and implementation standards, ASHRAE Transactions 95 (1) (1989) 789–797.
[4] M.A. Anderson, Energy cost allocation in multifamily buildings using comfort-based allocation devices, ASHRAE Transactions 99 (1) (1993) 899–906. [5] G.R. Guinn, L. Hummer, Testing and evaluation of Btu (heat) meters used for measuring solar system performance, ASHRAE Transactions 88 (2) (1982) 388–401. [6] R. Freischlag, CompuBill RBV-TR system technical note, Energy Billing Systems, Inc., Colorado Springs, CO, 1986. [7] M.J. Hewett, Analysis of error in using simple linear models to approximate the output of fan-coil units for energy cost allocation purposes, ASHRAE Transactions 100 (2) (1994) 148–160. [8] Y. Yao, Y. Hu, Z. Lian, Z. Hou, Method of thermal metering on the air side for fan coil units, ASHRAE Transactions 110 (2) (2004) 325–334. [9] J. Rekstad, M. Meir, A.R. Kristoffersen, Control and energy metering in low temperature heating systems, Energy and Buildings 35 (3) (2003) 281–291. [10] Y. Yao, Z. Lian, S. Liu, Z. Hou, Energy-cost allocation based on the theory of frequency response, Applied Energy 79 (4) (2004) 371–383. [11] G. Schramm, Marginal-cost pricing revisited, Energy Economics 13 (4) (1991) 245–249. [12] J. Sjodin, D. Henning, Calculating the marginal costs of a district-heating utility, Applied Energy 78 (1) (2004) 1–18. [13] O. Okka, Engineering Economy, Ankara, Turkey, 2000, pp. 211–217. [14] J. Pakanen, S. Karjalainen, Estimating static heat flows in buildings for energy allocation systems, Energy and Buildings 38 (9) (2006) 1044–1052. [15] L.K. Yu, G.Q. Zhang, X. Chen, Development of a web-based global optimal management system for district cooling, in: Proceedings of the 2003—Fourth International Symposium on Heating, Ventilating and Airconditioning, Beijing, China, (2003), pp. 973–977. [16] X.M. Ye, X.D. Zhang, W.F. Diao, A networked heat meter system for measuring the domestic heat supply, in: 2005 IEEE International Conference on Industrial Technology, ICIT 2005, Hong Kong, China, (2005), pp. 225–230. [17] L. Costa De Paula, J.M. Fernandes, On-line control systems using RS485. Instrument Society of America, in: ISA TECH/EXPO Technology Update Conference Proceedings, v 413 I, Houston TX, September 10–13, (2001), pp. 695–700. [18] Yixiong Hu, Ye Yao, Xinming chen, Design of thermal charging and management system based on RS-485 network, Computer Measurement & Control 10 (3) (2002) 186–188 (in Chinese). [19] J.C. Simpson, Customer energy services using power line carrier, in: Proceedings of the 1996 8th International Conference on Metering and Tariffs for Energy Supply, IEE Stevenage Engl, no. 426, 1996, pp. 254– 256 (IEE Conference Publication). [20] J. Newbury, W. Miller, Multiprotocol routing for automatic remote meter reading using power line carrier systems, IEEE Transactions on Power Delivery 16 (1) (2001) 1–5. [21] Yixiong Hu, Yao. Ye, The Design of air-conditioning charging meter and its communication system, Heating, Ventilation and Air-conditioning (HV&AC) 33 (4) (2003) 136–138 (in Chinese). [22] Sheng Li, Min Zhang, Research of power line direct sequence spectrum carrier communication system, Journal of Changsha University of Electric Power 14 (2) (1999) 138–140 (in Chinese).
Key technologies on heating/cooling cost allocation in multifamily housing Ye Yao a,*, Shiqing Liu b, Zhiwei Lian a a
Institute of Refrigeration & Cryogenics, Shanghai Jiao Tong University, Dongchuan Road No. 800, Shanghai 200030, China b Institute of Mathematics and Physics, Zhejiang Normal University, Zhejiang 321004, China Received 4 February 2007; received in revised form 21 March 2007; accepted 13 April 2007
Abstract Heating/cooling cost allocation is of growing concern in many countries because it contributes much to the energy conservation of central airconditioning system. This paper intends to summarize the current studies and techniques on the heating/cooling cost allocation and discuss about the key problems to them. The contents mainly include the following parts: (1) probing into the methods of heating/cooling measurement; (2) establishing the calculation model for thermal billing; (3) presenting several typical systems for heating/cooling cost allocation. The significance of the paper is to help the engineers in this field have a good idea of the current development of heating/cooling cost allocation and promote the application of the relevant technologies to practice. # 2007 Elsevier B.V. All rights reserved. Keywords: Heating/cooling; Measurement; Thermal energy; Price; Cost allocation system
1. Introduction Heating/cooling cost allocation refers to certain accounting procedures designed to divide the energy costs in centrally heated/cooled multifamily buildings among the individual apartments on the basis of use. Heating/cooling cost allocation not only contributes to energy conservation [1], but also brings about many other social and economic benefits, such as decreasing vacancy rates, enhancing the rent levels and improving the comfort of tenants [2]. Heating/cooling cost allocation in apartment buildings was firstly developed in the Western Europe. In the early 1970s, the European Economic Communities has formulated implementation guidelines to encourage allocation of heating/cooling cost in multifamily housing. As of 1979–1980, approximately 70% of multifamily buildings of three or more units in Germany had such allocation systems [3]. Many other countries in Europe, e.g. France, Switzerland, Austria and Greece, also required measurement and allocation of costs for central heating/cooling systems in new constructions beginning in the early 1980s. In USA, Heating/cooling cost allocation in multifamily housing
* Corresponding author. Tel.: +86 21 34204263. E-mail address: [email protected] (Y. Yao). 0378-7788/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2007.04.023
began as a cottage industry in the early 1980s as a result of the 1979 oil embargo [4]. In China, with the development of economy and improvement of people’s standard of living, centrally air-conditioned buildings have been rising in recent years. In order to advocate the consciousness of energy conservation among people, the government of China has also urged the implement of thermal energy cost allocation in centrally air-conditioned buildings since the end of 1990s. This paper will summarize the existing technologies and discuss over the key problems on the heating/cooling cost allocation. The contents mainly include: (1) probing into the methods of heating/cooling measurement; (2) establishing the calculation model for thermal billing; (3) presenting several typical systems for heating/cooling cost allocation. 2. Methods of heating/cooling measurement Impartial cost allocation depends on effective measurement. Over the years, an increasing number of approaches have been developed to measure the thermal energy use of apartment supplied by a central heating/cooling system. They can be categorized into two types: the straightforward and the backstair. The straightforward method computes the thermal energy consumption of an apartment based on the running conditions of the terminal heating/cooling units in the apartment. The
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Nomenclature A B c C d G h i K M N P q Q R t T U V W Y z
area of heat transfer (m2) price of primary energy (US$/kJ) specific heat (kJ/kg) cost for yielding thermal energy (US$) humidity of air (g/(kg dry air)) flow rate of fluid (kg/s) enthalpy (kJ/kg) yearly interest rate of bank overall coefficient of heat transfer (kW/(m2 8C)) overhead expenses per hour (US$) number of apartments involved in thermal cost allocation price (US$/kJ) thermal output of individual units (kJ) total amount of thermal energy produced per hour (kJ) thermal loss (kJ) temperature (8C) total operating time of the central system in a year (h) fixed/floating/cost per hour (US$) initial investment (US$) amount of heat gain or loss of the jth apartment during the billing time bill for thermal cost of individual apartment (US$) life cycle of facilities (year)
Greek letters b correction factor of thermal metering due to location of apartment in the building Dt interval time of calculation (Dt = t/n (n is one big integer)) e coefficient of performance of boilers or heat pumps h proportion of thermal load due to exposed structures in the total of the building k correction factor of heat exchange of individual units Subscripts a air h/c heating/cooling i inlet/entering j the jth apartment jk walls between the jth apartment and its adjacent ones k the kth apartment o outlet/leaving w water we exposed wall of apartment wr interior wall or roof of apartments
measured parameters may include the following variables: the inlet/outlet water temperature, the waterflow rate, the airflow rate, the inlet/outlet air temperature and humidityas well as the running time of the individual heating/cooling units. However, the backstair method measures the parameters other than the above variables. It realizes the thermal metering through special algorithm. Since the straightforward method is easy to understand and be accepted by average tenants, the thermal meters available in market nowadays are mostly based on the straightforward method. 2.1. Examples of straightforward method 2.1.1. Actual-Btu meters Actual-Btu meters usually measure the inlet water temperature, tw,i, the outlet water temperature, tw,o, and the water flow rate, Gw, as well as the running time, t, of the heating/ cooling units in an apartment. The consumption of heating/ cooling of a single apartment, qh/c, during the running time, t, can be calculated by: qh=c ðtÞ ¼ cw
n X
Gw ðkDtÞjtw;o ðkDtÞ tw;i ðkDtÞjDt
(1)
k¼1
In principle, Actual-Btu meters are of high accuracy, typically 98% [1]. However, in practice their accuracy is not as high as expected, especially when small temperature drops across an individual apartment loop. Guinn and Hummer [5] found that the errors of Actual-Btu meters could be as high as 30%. Still, Actual-Btu is considered as the most accurate method for thermal metering. The biggest shortcoming of such meters is of relatively high investment and difficult maintenance. 2.1.2. Relative-Btu meters Relative-Btu meters only measure the inlet water temperature, tw,i, and the outlet water temperature, tw,o, as well as the running time, t, of the individual heating/cooling units. It is assumed that the water flow rate passing through the heating/ cooling units be invariable. In such case, the thermal energy output of the terminal units in an apartment can be counted by: qh=c ðtÞ ¼ cw Gw
n X
jtw;o ðkDtÞ tw;i ðkDtÞjDt
(2)
k¼1
Relative-Btu meters may be valid only if there is no zone water valve in each heating/cooling units that adjusts the passing water flow rate. Otherwise, the metering accuracy will typically achieve above 90%. Otherwise, the error may exceed 50% [1,6]. A variation of Relative-Btu is only to measure the temperature of water that leaves each apartment. The entering water temperature of each apartment can be taken as the same, which equals to the supply water temperature of the central heating/cooling system. Obviously, Relative-Btu meters will be much cheaper than the Actual-Btu ones. 2.1.3. LMTD meters The method measures the inlet air temperature, ta,i, the outlet air temperature, ta,o, the inlet water temperature, tw,i, the outlet
Y. Yao et al. / Energy and Buildings 40 (2008) 689–696
water temperature, tw,o, and the running time, t, of the individual heating/cooling units. Then, use Eq. (3) to realize the thermal metering [7]: qh=c ðtÞ ¼ kh=c K h=c Ah=c
n X jLMTDðkDtÞjDt
(3)
k¼1
In Eq. (3), LMTD, namely Logarithmic Mean Temperature Difference, is usually used to calculate the heat transfer of the heat exchanger, which can be expressed by Eq. (3a): LMTDðkDtÞ ¼
½tw;i ðkDtÞ ta;o ðkDtÞ ½tw;o ðkDtÞ ta;i ðkDtÞ ln½ðtw;i ðkDtÞ ta;o ðkDtÞÞ=ðtw;o ðkDtÞ ta;i ðkDtÞÞ
(3a)
The most important step for the LMTD method is the determination of the total coefficient, K, and the heat transfer area, A, of the heating/cooling units. Since the total coefficient of heat transfer, K, is influenced by the flow rates of air and water, the LMTD meters are only fit for such systems that the water flow rate passing through the individual heating/cooling units changes very little. The airflow rates of the heating/ cooling units are usually divided into several levels. Each level of airflow rate will correspond to one value of heart transfer coefficient. When the consumer tunes the airflow rate from one level to another, the value of K will change correspondingly. Since LMTD just calculates the sensible thermal energy output of the heat exchanger, it will be much more accurate in heating season than in cooling one. In practice, the entering water temperature can be substituted by the supply water temperature of the boilers or the heat pumps. So, only three temperature sensors are needed for every apartment. 2.1.4. Air-side monitors The method mainly measures the conditions of inlet and outlet air of individual heating/cooling units. The measured parameters include: the inlet air temperature (ta,i), the inlet air humidity (da,i), the outlet air temperature (ta,o), the outlet air humidity (da,o), the airflow rate (Ga) and the running time (t). The thermal metering can be done using Eq. (4): n X Ga ðkDtÞjha;i ðkDtÞ ha;o ðkDtÞjDt qh=c ðtÞ ¼
(4)
k¼1
where ha;i ðkDtÞ ¼ ca ta;i ðkDtÞ þ ½2501 þ 1:84ta;i ðkDtÞda;i ðkDtÞ (4a) ha;o ðkDtÞ ¼ ca ta;o ðkDtÞ þ ½2501 þ 1:84ta;o ðkDtÞda;o ðkDtÞ (4b) Although air-side method is complicated and of high cost, it still has some merits such as convenience to install and maintain. In practice, the airflow rate, Ga, can be obtained from the level of airflow rate of the heating/cooling units. Hence, only two temperature sensors together with two humidity sensors are needed for this method.
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Another version of air-side method was put forward and studied in literature [8]. It only measures the temperature and the humidity of inlet air of individual heating/cooling units and realizes the thermal metering together with the other information that obtains from the central hydronic cooling/ heating systems through network communication. The method may be fit for such system where there are no local valves in the individual heating/cooling units. Theoretically, the errors of the method can be about 25% in most cases [8]. 2.1.5. Elapsed time meters The method just counts the running time of the heating/ cooling units in the apartment. Essentially, it does not measure the amount of heat delivered, but provide an estimate. Big metering errors will be caused by the elapsed time method because there may exist great differences among the terminal heat exchangers in thermal characteristic, and the conditions of cooling/heating water that enters into the apartments will be different from one to another. In spite of this, elapsed time meters are still popular in China due to their low investment. 2.2. Examples of backstair method 2.2.1. Comfort level monitors The idea of comfort level monitors is that ‘‘All residents with the same size apartment with the same average monthly setpoint pay the same amount.’’ Setpoint is used rather than space temperature because space temperature may be influenced by some factors, such as solar gain, the air infiltration from windows or doors. A comfort-based system using thermostat setpoint as an indication of system demand effectively eliminates building variables. The thermostat setpoint in each apartment is transduced from a potentiometer attached to the thermostat lever arm and then is transmitted to a central processor over building telephone lines. Comfort-based systems have been used and readily accepted by the residents in France for many years [4]. It would be more valid if the comfort level meters were used together with the excellent control system for indoor air temperature [9]. 2.2.2. Thermal metering based on load calculation The method counts the amount of thermal energy consumption in an individual apartment through calculating the heating/cooling load of the apartment during the use time. The measured parameters include the solar radiation intensity and the temperatures of indoor air and outdoor air. The authors ever studied the thermal metering method based on the theory of frequency response [10]. Experiments has been done in a residential building to manifest that heating/cooling load calculation may be a promising way in the thermal metering of residential apartments or office rooms. 3. Price of thermal energy A basic presupposition here is that optimal prices from a societal point of view should equal to short-range marginal costs (SRMC) of district cooling/heating generation [11]. These
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prices reflect the scarcity of resources in society, and are the best means for optimal resource allocation. However, such prices do not guarantee full cost coverage for the producer [12]. The price for cooling and heating is defined as the cost for every unit yielding thermal energy, which can be expressed as: Ph=c ¼
C h=c Qh=c
(5)
The cost of thermal energy, Ch/c, produced by the central heating/cooling system consists of two parts: one is named as fixed cost (Ufixed) that mainly includes the depreciation of facilities and the interest of investment and all the overhead expenses; the other is named as floating cost (Ufloating) that mainly includes the operating charges. C ¼ U fixed þ U floating
V½iði þ 1Þz =½ði þ 1Þz 1 þM T h=c
(7)
The floating cost, Ufloating, is correlative with the price of primary energy (B), the coefficient of performance of boilers or heat pumps (eh/c) and the total amount of thermal energy produced per year (Qh/c), which can be expressed as: U floating ¼
BQh=c eh=c
(8)
Combining Eqs. (5)–(8), the price of thermal energy produced by the central heating/cooling system can be written as: Ph=c ¼
(1) The initial investment of the central heating/cooling system, V; (2) The price of electrical energy or fuel, B; (3) The coefficient of performance of boilers or heat pumps, eh/c; (4) The amount of thermal energy produced the central heating/ cooling system per hour, Qh/c; (5) The yearly interest rate of bank, i; (6) The overhead expenses for management per hour, M.
(6)
According to the theory of engineering economy [13], the fixed cost per day, Ufixed, can be expressed as: U fixed ¼
Normally, the total operating time of the central heating/ cooling system in a year, Th/c, is settled by company. Thus, the price of thermal energy (Ph/c) is mainly related to the following factors:
V½iði þ 1Þz =½ði þ 1Þz 1 þ T h=c M B þ T h=c Qh=c eh=c
(9)
The price of thermal energy (Ph/c) in a day may change from hour to hour because the coefficient of performance of boilers or heat pumps (eh/c) fluctuates all the time. To illustrate the price model of thermal energy, one central air-conditioning system is taken as an example. The airconditioning system provides heating/cooling energy for 250 units apartments that are installed with FP600-type fan-coil units. The main equipments and initial investment of the system are listed in Table 1. The prices in Table 1 were provided by the East China Architecture Design Institution according to Chinese market. The exchange rate of US$ to RMB was set as 8.0. The coefficients of performance of the heat pump under different capacity ratio are shown in Table 2. The heat pumps, the cooling water pumps, the chilled/hot water pumps and the cooling tower are in operation during the cooling season, While in the heating season, the heat pumps are converted into the water-source ones and the cooling tower stops running. When the cooling/heating load demand exceeds 800 kW/900 kW, two heat pumps together with two cooling water pumps and two chilled/hot water pumps will be started.
Table 1 Equipments and initial total investment of one central air-conditioning system Items
Technical property
Number (set)
Investment (US$)
Screw heat pump
Rated cooling capacity: 774 kW Rated heating capacity: 897 kW Input electrical power: 160 kW
2
130,000
Cooling tower
Maximum water volume: 86.7 kg/s Input electrical power: 11.2 kW
2
15,000
Cooling water pump
Rated water volume: 87.5 kg/s Input electrical power: 30 kW
2
3,340
Chilled/hot water pump
Rated water volume: 70.8 kg/s Input electrical power: 22 kW
2
3,060
FP600 fan-coil unit
Heat capacity: 5.593 kW Input electrical power: 102.5 W
250
20,000
Pipes, valves and other fittings Charges for electrical distribution Charges for excess capacity of electricity Installment
– – – –
– – – –
14,700 32,712 20,445 21,500
Total
–
–
260,757
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Table 2 Coefficients of heat pump under different capacity rates Capacity rate (%) Compressor power input (kW) Cooling capacity (kW) ec Heating capacity (kW) eh
20 28.8 89.9 3.12 112.9 3.92
30 35.2 120.4 3.42 152.8 4.34
40 43.2 160.3 3.71 197.9 4.58
Otherwise, only one heat pump together with one cooling water pump and one chilled/hot water pump are operating. The cooling time of the system usually begins from 1 June to 1 October, and the heating time from 1 December this year to 1 March next year. The running time of the central heating/ cooling system in a day is set as 18 h, and the total operation time in a year is about 3180 h (Th/c = 3180 h). Assuming that the interest rate (i) is 0.005, the life cycle (z) is considered as 20 years, the overhead expenses (M) equals to US$ 15 h1, and the price of primary energy (B) is defaulted as US$ 0.1 kW h1, the hourly price of yielding thermal energy can be calculated using Eq. (9) with respect to the amount of yielding thermal energy and the hourly Coefficient of Performance (COP) of the heat pumps. The hourly cooling and heating energy produced by the heat pumps and the hourly COP of the system in one running day are plotted in Figs. 1 and 3, respectively. And the corresponding hourly price of cooling and heating energy are shown in Figs. 2 and 4, respectively. Seen from Figs. 1–4, the bigger amount of thermal energy produced by the central
Fig. 1. Hourly cooling energy produced and hourly coefficient of performance of the system in one day of August.
Fig. 2. Hourly price of cooling energy in the day of August.
50 54.4 210.5 3.87 260.6 4.79
60 68 277.4 4.08 337.3 4.96
70 82.4 348.6 4.23 422.7 5.13
80 100.8 439.5 4.36 529.2 5.25
90 128 600.3 4.69 701.4 5.48
100 160 787.2 4.92 910.4 5.69
heating/cooling system, the lower price of thermal energy will be. It accords with the general phenomenon of economics. 4. Individual thermal billing 4.1. Basic calculation method Based on the individual thermal metering and the price of thermal energy, the basic model for individual thermal billing, Yj, can be expressed as: R Y j ¼ Ph=c qh=c; j þ (10) N In Eq. (10), R denotes the thermal energy loss due to the heat exchange between chilled/hot pipes and the environment, which can be counted indirectly by Eq. (11): R ¼ Qh=c
N X qh=c; j
(11)
j¼1
Fig. 3. Hourly heating energy produced and hourly coefficient of performance of the system in one day of November.
Fig. 4. Hourly price of heating energy in the day of November.
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The basic model for thermal billing, in this paper, sticks to the principle that the tenants should pay equal cost for equal thermal energy use. In practice, some other detailed problems should be considered.
In residential building, the exposed structures may consume most of the heating/cooling energy of the apartment. Taking the apartment with the least exposed surface area as the standard one, the correction factor, b, for the other apartments can be expressed as:
4.2. Problem to indirect heat delivery In the apartment buildings, a certain amount of heat is delivered by indirect path, e.g. heat transferred through the wall from the warmer apartment to the other adjacent ones, and the warm air rising from lower apartments to the higher ones. These heat flows cannot be measured directly. So, proper adjustments for indirect heat delivery among the apartments should be made to guarantee the perfect allocation of thermal energy cost. The critical measure is to determine the static heat flow rates between neighboring rooms. Pakanen and Karjalainen [14] has focused on the heat transfer issues and put forward a new approach to solve it. Their approach is based on the proposed control techniques and the ARMAX-model describing dynamic behavior of heating/cooling power. The model is created for each room/flat of a building. Parameter values are identified using real-time measurements collected from each room/flat and its environment through a few days’ tuning. The prerequisite for successful estimation is the overall control and the precise adjustment of the room temperatures at specified level. When the heat delivery through the walls and roofs of apartments is taken into accounted, the billing Eq. (10) can be written as: R Y j ¼ Ph=c qh=c; j þ þ W j (12) N In Eq. (12), Wj is the amount of heat gain or loss of the jth apartment during the billing period, tbill: 8 m X > > K wr; jk A jk ð¯ta;k ¯ta; j Þ Heating time t > bill < k¼1 (13) Wj ¼ m X > > > tbill K wr; jk A jk ð¯ta; j ¯ta;k Þ Cooling time : k¼1
where m denotes the number of apartments that neighboring the jth apartment. ¯ta; j and ¯ta;k denote the mean indoor air temperature of the jth apartment and it adjacent ones during the billing time, tbill.
bj ¼
Awe; j Awe;standard Awe;total
(14)
where Awe,j, Awe,standard and Awe,total denote the area of exposed structure of the jth apartment, the standard apartment and the all apartments involved in the thermal energy cost allocation, respectively. Thus, the perfect individual billing equation may be written as: R Y j ¼ Ph=c ð1 þ bÞhqh=c; j þ ð1 hÞqh=c; j þ þ W j (15) N In Eq. (15), h is the ratio of heating/cooling load of the exposed structures to the total heating/cooling load of the building. To determine the value of h, the detailed design thermal load of the building can be referenced. 5. Typical system for thermal cost allocation Up to now, many advanced techniques have been applied to the heating/cooling cost allocation systems. Generally speaking, there are two types of system for the thermal cost allocation: one is network-based system; another is prepaid IC card system. 5.1. Network-based system Taking advantage of the technique of network, we can complete the remote thermal metering and charging without entering into the tenants’ apartment. Another merit of networkbased systems is that they can be fit for all metering methods and be propitious to improve the metering accuracy. Besides, through network, much useful information is recorded and saved real-timely with which the reasonable hourly price of thermal energy can be determined [15,16]. However, networkbased systems may have some shortcomings, e.g. relatively high investment, difficulty in maintenance and extend. In spite of their limitations, the network-based systems are still favored by people. Fig. 5 shows the schematic structure of the network-
4.3. Adjustment for the location of apartments The location in a building may produce important influence on the energy consumption of the apartments for heating/ cooling. Because apartments with different location in a building will have different exposed surface area, different air infiltration and different solar gain. These differences may cause substantial variations in the allocation bills from one apartment to another. For the sake of fairness, it is necessary to make the adjustment with respect to different location in the building such as the orientation, the floor, etc.
Fig. 5. Schematic for the thermal metering system based on the local network communication.
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based system for thermal metering and charging. In such system, the thermal meters with communication convertor are necessary. Obviously, the communication convertor will take the most important role in the network-based system. In this paper, two communication techniques, which may be potientially applied to the thermal metering and charging, are to be introduced briefly. 5.1.1. RS-485 communication It is well known that RS-485 is a comprehensive bidirectional and differential transmission data bus [17]. As a physical layer protocol, it provides half-duplex communication and multipoint links. The information can be sent or received through two wires. It has the features such as without charge accumulation, high capability of anti-jamming and long transfer distance. Although RS485 does not belong to field bus, it has strong life force because of the performance above. MAX485, as a kind of low-power transceiver for RS-485 and RS-232 communication, could be selected for the communication interface of the thermal meters. MAX485 sends and receives the information data by using only one transmission channel in a half-duplex mode The half-duplex mode has both merit and demerit. The advantage is that a transmission channel can operate using just two lines. This advantage must be weighed against the limitation that only one master on the sending side can operate at any given time. Fortunately, the limitation produces no influence on the work of network-based thermal metering and charging systems that are compose of one master machine and many sub-machines. The sub-machines, known as thermal meters, are responsible for the measurement of thermal energy consumption in individual apartment. They mainly include measurement component, computation component, data storage component and communication component with RS485 interface [18]. The master machine is usually in charge of many sub-machines (thermal meters). It can require communicating with any thermal meter in charge at any time through sending command. When one thermal meter receives the command, it will response to the master machine’s require and send the information in its memory chip to the master machine through RS-485 communication. The main task of the master machine is to monitor the thermal energy consumption of all apartments in a period of time, to determine the hourly price of thermal energy and to count the bills every tenant should pay for the thermal energy use. 5.1.2. Power line carrier communication A power line carrier (PLC) is communication equipment that operates at radio-frequencies, generally below 600 kHz, to transmit information over electric power transmission lines. The new communication technique has been developed very rapidly in recent years and been in wide field applications, such as energy services [19] and automatic remote meter reading [20,21]. The obvious advantage of power line carrier is that it need not construct an extra wiring, and hence save much labor force and time.The new ATL90 series Embedded PLC modem series is based on the Direct Sequence Spread Spectrum Technology [22]. The new technology in power line carrier
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communication is well known for its high immunity to electrical noise persistent in the power line. With the new solution, the form factor of the PLC modem is further reduced and its cost lowered. The Embedded PLC Modem is in the form of a ready-to-go circuit module, which is capable of transferring data over the power cable at the low voltage end of the power transformer of a 3-phase/4-wire distribution network. A pair of Embedded PLC Modems connected on the power line can provide low speed bi-directional data communication at a baud rate of 300/600 bps. It is built in a small form factor that can be easily integrated into and become part of the user’s power line data communication system. The modules provide bi-directional half-duplex data communication over the mains of any voltage up to 250 V ac, and for frequency of 50 or 60 Hz. Data communication of the modules is transparent to user’s data terminals and protocol independent; as a result, multiple units can be connected to the mains without affecting the operation of the others. The use of DSSS modulation technique ensures high noise immunity and reliable data communication. There is no hassle of building interface circuits. Interface to user’s data devices is a simple data-in and data-out serial link. It has a built-in on board ac coupling circuit, which allows direct and simple connection to the mains [20]. 5.2. Prepaid IC card system The outcome of the Prepaid integrated circuit (IC) card thermal metering system has changed the former paying way of the thermal energy thoroughly, from manually to automatically. The way it has changed brings much benefit to the heating/ cooling department. It not only strengthens the supervision, increases management efficiency, effectively prevents overdue bills, but also avoids the inconvenience of house call meter reading and decreases the capital of running the department. To make the prepaid IC card come to life, the most important point is to change the thermal meters that are now widely used, and make it easy for dismantling and card inserting. Besides, the thermal meter ought to have the function of automatic fee charging. In the Prepaid IC card thermal metering system: one user is assembled with one thermal meter and one card, to use thermal energy only by card. After the data in the card is transmitted to the thermal meter, the meter opens the valve and begins thermal supply, after the money is used up, it will automatically cut off thermal supply and you must buy thermal energy again to resume energy use. The working process of the IC card is depicted as follows: the users pay the fees to the thermal management department, which writes the amount of thermal into the IC card, and the users input the information of the IC card into the thermal meter, which can automatically begin thermal supply. During the period of thermal use, the microcomputer within the thermal meter will automatically check and subtract the used thermal energy, when the purchased thermal energy is used up, the intelligent thermal meter will cut off thermal automatically, and the user needs to buy thermal energy again. IC card can also record the operation
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conditions of the meter, to control total used thermal energy, total purchased thermal energy and the state of opening and closing of the valve by controlling computer or controlling software. 6. Conclusions This paper mainly aroused interest in the critical problems concerned about the heating/cooling cost allocation. The contents include: (1) Seven kinds of methods of thermal metering have been introduced in detail. At the same time, they are discussed and analyzed in terms of accuracy and investment. (2) The model of hourly price of thermal energy has been set up. One example is presented to expound the usage of the model. The results prove that the price model accords with the general phenomenon of thermal economics. The model will help us establish the reasonable and impartial price of thermal energy produced by the central systems of different kind. (3) The effective way of thermal billing of individual apartment is studied. Some field problems, such as the indirect heat delivery from one apartment to another and the adjustment for different location of apartment in a building, are discussed. The corresponding measures are suggested afterwards. (4) The typical systems for thermal cost allocation are presented. The network-based system, represented by the communication techniques of RS485 and power line carrier, and the prepaid IC card system are depicted in detail. Their technical properties are also introduced briefly.
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